Method for correcting input seismic traces from dissipative effects

ABSTRACT

A method and apparatus for correcting an input seismic trace. The method includes receiving the input seismic trace and creating a t by Q gather using the input seismic trace, where t represents traveltime, Q represents absorption parameter, and the t by Q gather has traveltime as the vertical axis and a ratio of t and Q as the horizontal axis. The ratio of t and Q is referred to as R. The method further includes applying an interpolation algorithm to the t by Q gather to derive a corrected input seismic trace.

BACKGROUND OF THE INVENTION

1. Field of the Invention

One or more embodiments of the present invention generally relate toseismic data processing, and more particularly to correcting seismicdata from dissipative effects.

2. Description of the Related Art

In seismic exploration, seismic data are obtained by first creating anartificial disturbance along the earth by use of dynamite or the like.The resulting acoustic waves travel downwardly in the earth and arereflected upward from subsurface reflecting interfaces. The reflectedwaves are received at detectors or geophones located along the groundand recorded in reproducible form. Ideally, the signals recorded at thedetectors would be exactly representative of the reflectioncharacteristics of the earth without the presence of any undesirablecomponents, such as noise or distortion.

Unfortunately, the signals recorded at the detectors often contain manyundesirable components which obscure the reflectivity function of theearth and prevent the finding of an area of the earth where oil and gasdeposits may be present. Several phenomena exist in causing distortionto the recorded signals. One such phenomenon is absorption, which causesthe actual loss of seismic energy by converting it to other forms ofenergy. This type of loss of seismic energy is generally known asintrinsic attenuation. A second phenomenon is intrabed multipleinterference. Intrabed multiple interference redistributes seismicenergy between downward and upward directions. This type of loss ofseismic energy is generally known as apparent attenuation. Apparentattenuation causes a progressive loss of the higher frequencies(broadening of the seismic wavelet) and an increasing phase distortionwith increasing traveltime for the seismic wavelet received.

The combination of intrinsic and apparent attenuation is generally knownas the earth filter. As a result of earth filtering, the seismic waveletis time varying. The existence of a time varying seismic waveletviolates a basic assumption of deconvolution theory and impairs theability to use deconvolution to determine the earth filtercharacteristics as part of a method of seismic interpretation.

One conventional approach to compensate for earth filter attenuation isdisclosed in Q-Adaptive Deconvolution, by D. Hale, Stanford ExplorationProject, Report 30, 1982. Hale discloses two iterative procedures forimplementing inverse Q-filtering. However, the procedures disclosed byHale make several assumptions which cause Hale to arrive at anapproximate dispersion relationship. Use of the approximate dispersionrelationship, in turn, degrades the value of the Q compensation obtainedby Hale.

Therefore, a need exists in the art for an improved method forcorrecting input seismic traces from dissipative effects through the useof Q-filtering.

SUMMARY OF THE INVENTION

One or more embodiments of the present invention are directed to afilter bank solution to Q-filtering for modeling, compensation andestimation of absorption in seismic data. Q-filtering generally refersto the application of time variant filters with amplitude and phasetransfer functions that conventionally depend on traveltime andabsorption parameter Q(t) as a function of that traveltime. Applicanthas observed that traveltime t and absorption parameter Q(t) are coupledparameters, and as a result, Q-filtering may be re-parameterized as aratio (R) of traveltime t and absorption parameter Q(t), which may beexpressed as R=t/Q(t). In this manner, various embodiments of theinvention propose a one-dimensional parametric family of filters, whichmodifies Q-filtering from a time variant filtering operation to theapplication of a range of time-invariant filters.

In one embodiment, the present invention is directed to a method forcorrecting an input seismic trace. The method includes receiving theinput seismic trace and creating a t by Q gather using the input seismictrace, where t represents traveltime, Q represents absorption parameter,and the t by Q gather has traveltime as the vertical axis and a ratio oft and Q as the horizontal axis. The ratio of t and Q is referred to asR. The method further includes applying an interpolation algorithm tothe t by Q gather to derive a corrected input seismic trace.

In another embodiment, the method for correcting an input seismic traceincludes receiving the input seismic trace, filtering the input seismictrace using an amplitude correction filter expressed asA_(R)(ƒ)=exp(sgnπƒR) and a phase correction filter expressed as

${\varphi_{R}(f)} = {{sgn}\; 2f\;{\ln\left( \frac{f_{\max}}{f} \right)}R}$to generate a plurality of filtered input seismic traces in the timedomain, where f represents the frequency of the input seismic trace,f_(max) represents the maximum frequency of the input seismic trace, andR represents a ratio between traveltime and absorption parameter. Themethod further includes applying an interpolation algorithm to filteredinput seismic traces in the time domain to derive a corrected inputseismic trace.

In yet another embodiment, embodiments of the invention are directed toa method for processing an input seismic trace. The method includesreceiving the input seismic trace and creating a t by Q gather using theinput seismic trace, where t represents traveltime, Q representsabsorption parameter, and the t by Q gather has traveltime as thevertical axis and a ratio of t and Q as the horizontal axis. The ratioof t and Q is referred to as R.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention can be understood in detail, a more particular description ofthe invention, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlytypical embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

FIG. 1 illustrates a schematic view of marine seismic surveying forwhich various embodiments of the invention may be used.

FIG. 2 illustrates a method for correcting an input seismic trace fromdissipative effects in accordance with one embodiment of the invention.

FIG. 3 illustrates a method for correcting an input seismic trace fromdissipative effects in accordance with another embodiment of theinvention.

FIG. 4A illustrates t by Q gather in accordance with one embodiment ofthe invention.

FIG. 4B illustrates t by Q gather in accordance with another embodimentof the invention.

FIG. 5 illustrates a flow diagram of a method for generating anestimated value of Q(t) in accordance with one embodiment of theinvention.

FIG. 6 illustrates a flow diagram of a method for generating anestimated value of Q(t) in accordance with another embodiment of theinvention.

FIG. 7 illustrates a computer network, into which embodiments of theinvention may be implemented.

DETAILED DESCRIPTION

One or more embodiments of the invention may be used in connection withvarious seismic surveying, such as marine seismic surveying, landseismic surveying, seabed seismic surveying, bore hole seismic surveyingand the like. FIG. 1 illustrates a schematic view of marine seismicsurveying 100 for which various embodiments of the invention may beused. Subterranean formations to be explored, such as 102 and 104, liebelow a body of water 106. Seismic energy sources 108 and seismicreceivers 110 are positioned in the body of water 106, typically by oneor more seismic vessels (not shown). A seismic source 108, such as anair gun, creates seismic waves in the body of water 106 and a portion ofthe seismic waves travels downward through the water toward thesubterranean formations 102 and 104 beneath the body of water 106. Whenthe seismic waves reach a seismic reflector, a portion of the seismicwaves reflects upward and a portion of the seismic waves continuesdownward. The seismic reflector can be the water bottom 112 or one ofthe interfaces between subterranean formation, such as interface 114between formations 102 and 104. When the reflected waves travelingupward reach the water/air interface at the water surface 116, amajority portion of the waves reflects downward again. Continuing inthis fashion, seismic waves can reflect multiple times between upwardreflectors, such as the water bottom 112 or formation interface 114, andthe downward reflector at the water surface 116 above. Each time thereflected waves propagate past the position of a seismic receiver 110,the receiver 110 senses the reflected waves and generates representativeseismic signals. These seismic signals may then be used to yieldvaluable information regarding the geophysical characteristics of theexplored subterranean formations.

FIG. 2 illustrates a method 200 for correcting an input seismic tracefrom dissipative effects in accordance with one embodiment of theinvention. Steps 210 through 249 are directed toward creating a t by Qgather, which is defined by an R axis and a t axis, where R=t/Q, and trepresents traveltime. Q represents absorption parameter and may oftenbe referred to as the seismic quality factor. Q may also be a functionof traveltime t and as such be referred to as Q(t). At step 210, aninput seismic trace and an absorption parameter Q(t) are received. Theabsorption parameter Q(t) may be retrieved from a table stored in a database. In one embodiment, the absorption parameter Q(t) may be a range ofabsorption parameter Q(t) values, which includes minimum and maximumQ(t) values. In yet another embodiment, the absorption parameter Q(t)value may be determined using method 500 or method 600, as describedbelow with reference to FIGS. 5 and 6.

At step 220, a sampling interval along the R axis, ΔR, is calculatedaccording to

$\begin{matrix}{{{\Delta\; R} = \frac{\pi\; e}{2\; f_{\max}}},} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$where ƒ_(max) represents an estimate of the maximum frequency in theinput seismic trace. For example, the sampling interval along the R axisis about 0.043 seconds for a maximum frequency of about 100 Hz. In oneembodiment, the largest sampling interval for which the t by Q gather isnot aliased is selected.

Equation 1 may be derived by analyzing a phase correction filter

$\begin{matrix}{{{\varphi_{R}(f)} = {{sgn}\; 2f\;{\ln\left( \frac{f_{c}}{f} \right)}R}},} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$where R=t/Q, f represents the frequency of the input seismic trace inthe frequency domain, f_(c) represents the cutoff frequency of the inputseismic trace, sgn=−1 when the filters are used for modeling absorptionand sgn=1 when the filters are used for compensation (i.e., inverseQ-filtering). The maximum frequency f_(max) of the input seismic tracemay be introduced into Equation 2 to distinguish the effect of thecutoff frequency f_(c) as a simple time variant time shift, which may beexpressed as:

$\begin{matrix}{{{\varphi_{R}(f)} = {{sgn}\; 2f\;{\ln\left( {\frac{f_{c}}{f}\frac{f_{\max}}{f_{\max}}} \right)}}}{R = {{{sgn}\; 2f\;{\ln\left( \frac{f_{\max}}{f} \right)}R} + {{sgn}\; 2f\;{\ln\left( \frac{f_{c}}{f_{\max}} \right)}{R.}}}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

The R value in the first portion of Equation 3 for which the phasereaches the value of 2π the first time is determined. It is observedthat this R value is the wavelength along the R axis of the periodiccomplex valued function e^(jφ) _(R) ^((ƒ)) and may be expressed as:

$\begin{matrix}{{\lambda(f)} = \frac{\pi}{f\;{\ln\left( \frac{f\;\max}{f} \right)}}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

The corresponding frequency along the R axis f_(R)(f) may be expressedas:

$\begin{matrix}{{f_{R}(f)} = {\frac{1}{\pi}f\;{\ln\left( \frac{f_{c}}{f} \right)}}} & \left( {{Equation}\mspace{14mu} 5} \right)\end{matrix}$Equation 5 is then solved for the maximum value of the frequency alongthe R axis as a function of the temporal frequencies between zero andf_(max). The maximum value of the R frequencies may be used to definethe sampling interval ΔR, which may be represented as:

$\begin{matrix}{{\Delta\; R} = \frac{1}{2\;{\max_{f}\left( {\frac{1}{\pi}f\;{\ln\left( \frac{f_{\max}}{f} \right)}} \right)}}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$The temporal frequency at which Equation 5 reaches its maximum value maybe estimated as:

$\begin{matrix}{\overset{\Cap}{f} = {{\mathbb{e}}^{({{\ln{(f_{\max})}} - 1})} = \frac{f_{\max}}{\mathbb{e}}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$Accordingly, substituting Equation 7 into Equation 6 leads to

${\Delta\; R} = {\frac{\pi\;{\mathbb{e}}}{2f_{\max}}.}$

At step 230, a plurality of R values are determined using t, Q(t) andthe sampling interval ΔR. In one embodiment, n+1 R values aredetermined, where

${R_{\min} = {\min\left( \frac{t}{Q(t)} \right)}},{R_{\max} = {\max\left( \frac{t}{Q(t)} \right)}},{and}$R_(n) = R_(min) + (n)Δ Rwhere n=0, 1, 2, 3 . . . until R_(n)=R_(max). At n=0, R₀=R_(min).

At step 240, the input seismic trace is filtered using an amplitudecorrection filter A_(R)(ƒ)=exp(sgnπƒR), the phase correction filter

${{\varphi_{R}(f)} = {{sgn}\mspace{11mu} 2f\;{\ln\left( \frac{f_{\max}}{f} \right)}R}},$and the R values generated at step 230, where f represents the frequencyof the input seismic trace, f_(max) represents the maximum frequency ofthe input seismic trace, sgn=−1 when the filters are used for modelingabsorption and sgn=1 when the filters are used for compensation (i.e.,inverse Q filtering). In one embodiment, the input seismic trace may befiltered using the above mentioned amplitude and phase correctionfilters by first transforming the input seismic trace to the frequencydomain (step 242). In one embodiment, the input seismic trace istransformed using a fast Fourier transform. Then, at step 244, theamplitude and phase correction filters are computed using the first Rvalue. At step 246, the result of step 244 is multiplied with the inputseismic trace in the frequency domain. In one embodiment, the result ismultiplied with the complex numbers of the input seismic trace in thefrequency domain. The result of step 244 may be capped by a maximumvalue. At step 248, a determination is made as to whether another Rvalue from the n+1 R values generated at step 230 needs to be processed.If the answer is in the affirmative, processing returns to step 244. Inthis manner, processing continues until all of the n+1 R values havebeen processed through steps 244-248, thereby generating an n+1 filteredinput seismic traces in the frequency domain. In this manner, the inputseismic trace may be filtered in the frequency domain. At step 249, then+1 filtered input seismic traces are transformed to the time domain,thereby generating an n+1 filtered input seismic traces in the timedomain, which make up the t by Q gather. In one embodiment, thetransformation to the time domain is performed using an inverse fastFourier transform.

At step 250, an interpolation algorithm is applied to the t by Q gatheralong an R(t) curve to derive a corrected input seismic trace, whereR(t)=t/Q(t). The interpolation algorithm used in step 250 may be alinear interpolation or any other interpolation algorithm commonly knownby those skilled in the art. The application of the interpolationalgorithm may also be known as “slicing through” the t by Q gather alongthe R(t) curve. Steps 210 through 250 may be repeated for other inputseismic traces. In this manner, the corrected input seismic trace may bederived by taking for each time sample of the filtered input seismictrace, the corresponding time sample from the filtered input seismictraces closest to the R(t) curve.

FIG. 4A illustrates a t by Q gather 400 in accordance with oneembodiment of the invention. The t by Q gather 400 is comprised within ahorizontal axis of R and a vertical axis of traveltime t. The t by Qgather is made up of n+1 filtered input seismic traces 410. The firstfiltered input seismic trace 410 is generated using the R_(min) and thelast filtered input seismic trace 410 is generated using R_(max). The tby Q gather also includes an R(t) curve 420 intersecting the n+1filtered input seismic traces 410. The t by Q gather may be slicedthrough along the R(t) curve 420 to generate the corrected input seismictrace.

In an embodiment in which the cutoff frequency f_(c) is not the same asthe maximum frequency f_(max), the t by Q gather may be “sliced through”an R′(t) curve, which may be expressed as R′(t)=R(t)+sgnτ(R(t)), wheresgnτ(R(t)) is derived from

${{\tau(R)} = {{sgn}\frac{1}{\pi}{\ln\left( \frac{f_{c}}{f_{\max}} \right)}R}},$which is the equivalent to the time shift portion of Equation 3. Anexample of an R′(t) curve 460 with respect to an R(t) curve 420 isillustrated in FIG. 4B. As illustrated, R′(t) curve 460 differs fromR(t) curve 420 by a time shift of sgnτ(R(t)).

FIG. 3 illustrates a method 300 for correcting an input seismic tracefrom dissipative effects in accordance with another embodiment of theinvention. Steps 310 through 330 perform the same steps as steps 210through 230. Accordingly, details of steps 310 through 330 may be foundwith reference to steps 210 through 230. At step 340, the input seismictrace is filtered using an amplitude correction filterA_(R)(ƒ)=exp(sgnπƒR), a phase correction filter

${{\varphi_{R}(f)} = {{sgn}\; 2\; f\;{\ln\left( \frac{f\mspace{11mu}\max}{f} \right)}R}},$and the R values generated at step 330. In one embodiment, the inputseismic trace may be filtered by first applying an inverse Fouriertransform to the amplitude and phase correction filters for all R values(step 342). In this manner, the amplitude and phase correction filtersare transformed to the time domain. At step 344, the result of step 342is convolved with the input seismic trace to generate the n+1 filteredinput seismic traces in the time domain, which make up the t by Qgather. The input seismic trace may also be filtered with other types ofconvolution filters commonly known by persons with ordinary skill in theart. At step 350, an interpolation algorithm is applied to the t by Qgather along the R(t) curve to derive a corrected input seismic trace.Step 350 performs the same step as step 250. Accordingly, details ofstep 350 may be found with reference step 250.

FIG. 5 illustrates a flow diagram of a method 500 for generating anestimated value of Q(t) in accordance with one embodiment of theinvention. Steps 510 through 540 are directed toward creating a t by Qgather. At step 510, an input seismic trace is received. At step 520, asampling interval along the R axis, ΔR, is calculated according to

${\Delta\; R} = {\frac{\pi\; e}{2\; f_{\max}}.}$At step 530, a plurality of R values are determined using t, thesampling interval ΔR, and a range of Q(t) values, e.g., minimum andmaximum Q(t) values, for a desired subterranean region. Steps 510through 530 are the same as steps 210 through 230 except that thetypical range of Q(t) values for the desired subterranean region is usedto calculate the R values, as opposed to a single Q(t) value.Accordingly, details of steps 510 through 530 may be found withreference steps 210 through 230.

At step 540, the input seismic trace is filtered using an amplitudecorrection filter A_(R)(ƒ)=exp(sgnπƒR), a phase correction filter

${{\varphi_{R}(f)} = {{sgn}\; 2\; f\;{\ln\left( \frac{f_{\max}}{f} \right)}R}},$and the R values generated at step 530. The input seismic trace may befiltered using the fast Fourier transform, as described in method 200,or the convolution algorithm, as described in method 400. At the end ofstep 540, an n+1 filtered input seismic traces in the time domain aregenerated to create the t by Q gather. Steps 510 through 540 may berepeated to generate a plurality of t by Q gathers.

At step 550, the t by Q gather is displayed on a display medium, such asa screen or a visualization center. At step 560, two or more desiredfeatures in the t by Q gather are identified. The desired features maybe identified using markers or other identifiers. At step 570, thedesired markers are connected to generate an R(t) curve. The desiredmarkers may be connected by a linear line, or any other curve fittingalgorithm commonly known by persons with ordinary skill in the art. Atstep 580, the Q(t) is determined by dividing the traveltime t by R(t).

FIG. 6 illustrates a flow diagram of a method 600 for generating anestimated value of a time variant Q(t) in accordance with anotherembodiment of the invention. At step 610, a one dimensional inputseismic trace, i.e., based on traveltime t, is received. At step 620, atime variant Fourier transform is applied to the input seismic trace togenerate a time variant amplitude spectrum of the input seismic trace,which may be represented as X(t, f). The time variant amplitude spectrumof the input seismic trace X(t, f) may be expressed as:X(t,f)=A(t,f)W(f)I(f)  (Equation 8),where A(t, f) represents a time variant exponential absorption term,W(f) represents a time invariant source wavelet, and I(f) represents atime-invariant reflectivity. The time variant exponential absorptionterm A(t, f) may be expressed as:A(t,ƒ)=exp(−#ƒR(t))  (Equation 9),where

${R(t)} = {\frac{t}{Q(t)}.}$

At step 630, the natural logarithm of the time variant amplitudespectrum of the input seismic trace X(t, f) is calculated and the resultis divided by −πf. Step 630 may be expressed as:

$\begin{matrix}{{S\left( {t,f} \right)} = {\frac{\ln\left( {X\left( {t,f} \right)} \right)}{{- \pi}\; f} = {{R(t)} + {{c(f)}.}}}} & \left( {{Equation}\mspace{14mu} 10} \right)\end{matrix}$

At step 640, a least squares power series approximation to S(t, f) isperformed to generate a plurality of power series coefficients s_(i),i.e., s₀, s₁, s₂, . . . s_(n). The least squares estimate to the powerseries coefficients may be computed by solving the followingminimization problem:

$\left. {{{S\left( {t,f} \right)} - {\sum\limits_{i = 0}^{n}{s_{i}t^{i}}}}}^{2}\rightarrow{\min.} \right.$In one embodiment, the least squares powers series is of a low order,i.e., n is a small number, e.g., from about 2 to about 8.

S(t, f) may also be expressed as: S(t, ƒ)=R(t)+c(ƒ) where c(f)represents an unknown frequency dependent constant. At step 650, theunknown frequency dependent constant c(f) is set to be equal to thefirst power series coefficient s₀. At step 660, a power seriesapproximation to R(t) is determined by performing a power seriesapproximation to S(t, f) with the index starting from 1, as opposed to0, i.e., without using the first power series coefficient s₀. The powerseries approximation to R(t) may be expressed as:

${\hat{R}(t)} = {\sum\limits_{i = 1}^{n}{s_{i}{t^{i}.}}}$In this manner, the ratio of traveltime t and time variant Q(t) may beapproximated by the power series approximation.

At step 670, the traveltime t is divided by R(t) to generate anestimated value of the time variant Q(t).

FIG. 7 illustrates a computer network 700, into which embodiments of theinvention may be implemented. The computer network 700 includes a systemcomputer 730, which may be implemented as any conventional personalcomputer or workstation, such as a UNIX-based workstation. The systemcomputer 730 is in communication with disk storage devices 729, 731, and733, which may be external hard disk storage devices. It is contemplatedthat disk storage devices 729, 731, and 733 are conventional hard diskdrives, and as such, will be implemented by way of a local area networkor by remote access. Of course, while disk storage devices 729, 731, and733 are illustrated as separate devices, a single disk storage devicemay be used to store any and all of the program instructions,measurement data, and results as desired.

In one embodiment, seismic data from hydrophones are stored in diskstorage device 731. The system computer 730 may retrieve the appropriatedata from the disk storage device 731 to perform the seismic tracescorrection method according to program instructions that correspond tothe methods described herein. The program instructions may be written ina computer programming language, such as C++, Java and the like. Theprogram instructions may be stored in a computer-readable memory, suchas program disk storage device 733. Of course, the memory medium storingthe program instructions may be of any conventional type used for thestorage of computer programs, including hard disk drives, floppy disks,CD-ROMs and other optical media, magnetic tape, and the like.

According to the preferred embodiment of the invention, the systemcomputer 730 presents output primarily onto graphics display 727, oralternatively via printer 728. The system computer 730 may store theresults of the methods described above on disk storage 729, for lateruse and further analysis. The keyboard 726 and the pointing device(e.g., a mouse, trackball, or the like) 725 may be provided with thesystem computer 730 to enable interactive operation.

The system computer 730 may be located at a data center remote from thesurvey region. The system computer 730 is in communication withhydrophones (either directly or via a recording unit, not shown), toreceive signals indicative of the reflected seismic energy. Thesesignals, after conventional formatting and other initial processing, arestored by the system computer 730 as digital data in the disk storage731 for subsequent retrieval and processing in the manner describedabove. While FIG. 7 illustrates the disk storage 731 as directlyconnected to the system computer 730, it is also contemplated that thedisk storage device 731 may be accessible through a local area networkor by remote access. Furthermore, while disk storage devices 729, 731are illustrated as separate devices for storing input seismic data andanalysis results, the disk storage devices 729, 731 may be implementedwithin a single disk drive (either together with or separately fromprogram disk storage device 733), or in any other conventional manner aswill be fully understood by one of skill in the art having reference tothis specification

While the foregoing is directed to embodiments of the present invention,other and further embodiments of the invention may be devised withoutdeparting from the basic scope thereof, and the scope thereof isdetermined by the claims that follow.

What is claimed is:
 1. A method for correcting an input seismic trace, comprising: receiving the input seismic trace; creating, using a computer, a t by Q gather using the input seismic trace, wherein t represents traveltime, Q represents absorption parameter, and the t by Q gather has traveltime as the vertical axis and a ratio of t and Q as the horizontal axis, wherein the ratio of t and Q is referred to as R; and applying an interpolation algorithm to the t by Q gather to derive a corrected input seismic trace.
 2. The method of claim 1, wherein the interpolation algorithm is a linear interpolation algorithm.
 3. The method of claim 1, wherein creating the t by Q gather comprises receiving an absorption parameter Q(t).
 4. The method of claim 1, wherein creating the t by Q gather further comprises calculating a sampling interval along the horizontal axis.
 5. The method of claim 4, wherein the sampling interval is calculated using an equation ${{\Delta\; R} = \frac{\pi\; e}{2f_{\max}}},$ wherein ΔR represents the sampling interval and f_(max) represents the maximum frequency of the input seismic trace.
 6. The method of claim 4, wherein the sampling interval is the largest interval for which the t by Q gather is not aliased.
 7. The method of claim 4, wherein creating the t by Q gather further comprises determining a plurality of R values using t, Q(t) and the sampling interval.
 8. The method of claim 7, wherein creating the t by Q gather comprises filtering the input seismic trace using an amplitude correction filter expressed as A_(R)(ƒ)=exp(sgnπƒR) and a phase correction filter expressed as ${{\varphi_{R}(f)} = {{sgn}\; 2\; f\;{\ln\left( \frac{f_{\max}}{f} \right)}R}},$ wherein f represents the frequency of the input seismic trace and f_(max) represents the maximum frequency of the input seismic trace.
 9. The method of claim 8, wherein filtering the input seismic trace comprises: transforming the input seismic trace to a frequency domain; computing the amplitude and phase correction filters for each R value; and multiplying the result with the input seismic trace in the frequency domain to generate a plurality of filtered input seismic traces in the frequency domain.
 10. The method of claim 9, wherein filtering the input seismic trace further comprises transforming the filtered input seismic traces in the frequency domain to a time domain.
 11. The method of claim 10, wherein the filtered input seismic traces in the time domain make up the t by Q gather.
 12. The method of claim 9, wherein filtering the input seismic trace further comprises transforming the filtered input seismic traces in the frequency domain to a time domain using an inverse fast Fourier transform.
 13. The method of claim 8, wherein filtering the input seismic trace comprises: transforming the input seismic trace to a frequency domain; computing the amplitude and phase correction filters for each R value; and multiplying the result with the complex numbers of the input seismic trace in the frequency domain to generate a plurality of filtered input seismic traces in the frequency domain.
 14. The method of claim 8, wherein filtering the input seismic trace comprises applying an inverse Fourier transform to the amplitude and phase correction filters for each R value.
 15. The method of claim 1, wherein creating the t by Q gather comprises filtering the input seismic trace using an amplitude correction filter expressed as A_(R)(ƒ)=exp(sgnπƒR), wherein f represents the frequency of the input seismic trace.
 16. The method of claim 1, wherein creating the t by Q gather comprises filtering the input seismic trace using a phase correction filter expressed as ${{\varphi_{R}(f)} = {{sgn}\; 2\; f\;{\ln\left( \frac{f_{\max}}{f} \right)}R}},$ wherein f represents the frequency of the input seismic trace and f_(max) represents the maximum frequency of the input seismic trace.
 17. The method of claim 1, wherein creating the t by Q gather comprises filtering the input seismic trace using an amplitude correction filter expressed as A_(R)(ƒ)=exp(sgnπƒR) and a phase correction filter expressed as ${{\varphi_{R}(f)} = {{sgn}\; 2\; f\;{\ln\left( \frac{f_{\max}}{f} \right)}R}},$ wherein f represents the frequency of the input seismic trace and f_(max) represents the maximum frequency of the input seismic trace.
 18. The method of claim 17, wherein filtering the input seismic trace comprises transforming the amplitude and phase correction filters to a time domain.
 19. The method of claim 18, wherein filtering the input seismic trace further comprises convolving the input seismic trace with the amplitude and phase correction filters in the time domain to generate a plurality of filtered input seismic traces in the time domain.
 20. The method of claim 19, wherein the filtered input seismic traces in the time domain make up the t by Q gather.
 21. The method of claim 1, wherein creating the t by Q gather comprises transforming the input seismic trace to a frequency domain.
 22. The method of claim 1, wherein creating the t by Q gather comprises transforming the input seismic trace to a frequency domain using a fast Fourier transform.
 23. A method for processing an input seismic trace, comprising: receiving the input seismic trace; and creating, using a computer, a t by Q gather using the input seismic trace, wherein t represents traveltime, Q represents absorption parameter, and the t by Q gather has traveltime as the vertical axis and a ratio of t and Q as the horizontal axis, wherein the ratio of t and Q is referred to as R.
 24. The method of claim 23, wherein creating the t by Q gather comprises: transforming the input seismic trace to a frequency domain; filtering the input seismic trace in the frequency domain through an amplitude correction filter and a phase correction filter to generate a plurality of filtered input seismic traces in the frequency domain; and transforming the filtered input seismic traces in the frequency domain to a time domain.
 25. A non-transitory computer-readable medium having stored thereon computer-executable instructions which, when executed by a computer, cause the computer to: receive the input seismic trace; and create a t by Q gather using the input seismic trace, wherein t represents traveltime, Q represents absorption parameter, and the t by Q gather has traveltime as the vertical axis and a ratio of t and Q as the horizontal axis, wherein the ratio of t and Q is referred to as R.
 26. The non-transitory computer-readable medium of claim 25, further comprising computer-executable instructions which, when executed by the computer, cause the computer to: apply an interpolation algorithm to the t by Q gather to derive a corrected input seismic trace.
 27. The non-transitory computer-readable medium of claim 25, wherein the computer-executable instructions which, when executed by the computer, cause the computer to create the t by Q gather comprises computer-executable instructions that cause the computer to receive an absorption parameter Q(t). 